Logistic distribution Probabilities
Calculator of Logistic distribution : probabilities, density function (PDF) and cumulative density function (CDF).
Logistic Distribution formulas
X : a random variable following a logistic distribution
`mu` : location parameter
s : scale parameter (s > 0)
Probability Density Function (PDF)
`f(x) = (e^(-(x-mu))/s)/(s*(1+e^(-(x-mu))/s)^2)`
Cumulative distribution function (CDF)
`F(x) = \int_-oo^x f(t)\ dt`
`F(x) = 1/(1+e^(-(x-mu))/s)`
Probabilities
Probability that X is greater than a :
`P(X > a) = 1 - F(a) = 1/(1+e^(a-mu)/s)`
Probability that X is less than b :
`P(X < b) = F(b) = 1/(1+e^(mu-b)/s)`
Probability that X lies between a and b :
`P(a < X < b) = F(b) - F(a)`
See also
Inverse Logistic distribution
Logistic distribution Chart
Statistics Calculators